Existence and global asymptotical stability of periodic solution for the T-periodic logistic system with time-varying generating operators and T0-periodic impulsive perturbations on banach space

Discrete Dynamics in Nature and Society

Volumn 2008, Issue , 2008, Pages

  Wang, JinRong ^a   Xiang, X ^a   Chen, Qian ^a  

^a GUIZHOU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50849113425     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2008/524945     Document Type: Article

References (24)

1. J. M. Cushing, "Periodic time-dependent predator-prey systems," SIAM Journal on Applied Mathematics, vol. 32, no. 1, pp. 82-95, 1977.
2. H. Amann, "Periodic solutions of semilinear parabolic equations," in Nonlinear Analysis: A Collection of Papers in Honor of Erich H. Rothe, pp. 1-29, Academic Press, New York, NY, USA, 1978.
3. L. H. Erbe and X. Liu, "Existence of periodic solutions of impulsive differential systems," Journal of Applied Mathematics and Stochastic Analysis, vol. 4, no. 2, pp. 137-146, 1991.
4. J. H. Liu, "Bounded and periodic solutions of di.erential equations in Banach space," Applied Mathematics and Computation, vol. 65, no. 1-3, pp. 141-150, 1994.
5. P. Sattayatham, S. Tangmanee, and W. Wei, "On periodic solutions of nonlinear evolution equations in Banach spaces," Journal of Mathematical Analysis and Applications, vol. 276, no. 1, pp. 98-108, 2002.
6. X. Xiang and N. U. Ahmed, "Existence of periodic solutions of semilinear evolution equations with time lags," Nonlinear Analysis: Theory, Methods & Applications, vol. 18, no. 11, pp. 1063-1070, 1992.
7. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK, 1993.
8. X. Liu, "Impulsive stabilization and applications to population growth models," The Rocky Mountain Journal of Mathematics, vol. 25, no. 1, pp. 381-395, 1995.
9. T. Yang, Impulsive Control Theory, vol. 272 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 2001.
10. L. Yong, C. Fuzhong, L. Zhenghua, and L. Wenbin, "Periodic solutions for evolution equations," Nonlinear Analysis: Theory, Methods & Applications, vol. 36, no. 3, pp. 275-293, 1999.
11. T. Naito, N. Van Minh, R. Miyazaki, and J. S. Shin, "A decomposition theorem for bounded solutions and the existence of periodic solutions of periodic differential equations," Journal of Differential Equations, vol. 160, no. 1, pp. 263-282, 2000.
12. W.Wei and X. Xiang, "Anti-periodic solutions for first and second order nonlinear evolution equations in Banach spaces," Journal of Systems Science and Complexity, vol. 17, no. 1, pp. 96-108, 2004.
13. C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Pure and Applied Mathematic, John Wiley & Sons, New York, NY, USA, 1976.
14. B. S. Goh, Management and Analysis of Biological Population, Elsevier, Amsterdam, The Netherlands, 1980.
15. M. Fan and K. Wang, "Optimal harvesting policy for single population with periodic coeffecients," Mathematical Biosciences, vol. 152, no. 2, pp. 165-177, 1998.
16. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Di.erential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Singapore, 1989.
17. N. U. Ahmed, "Some remarks on the dynamics of impulsive systems in Banach spaces," Dynamics of Continuous, Discrete & Impulsive Systems. Series A, vol. 8, no. 2, pp. 261-274, 2001.
18. J. H. Liu, "Nonlinear impulsive evolution equations," Dynamics of Continuous, Discrete and Impulsive Systems, vol. 6, no. 1, pp. 77-85, 1999.
19. X. Xiang and W.Wei, "Mild solution for a class of nonlinear impulsive evolution inclusions on Banach space," Southeast Asian Bulletin of Mathematics, vol. 30, no. 2, pp. 367-376, 2006.
20. D. Daners and P. K. Medina, Abstract Evolution Equations, Periodic Problems and Applications, vol. 279 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow, UK, 1992.
21. M. Farkas, Periodic Motions, vol. 104 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1994.
22. C. J. K. Batty, "Asymptotic behaviour of semigroups of operators," in Functional Analysis and Operator Theory, vol. 30 of Banach Center Publications, pp. 35-52, Polish Academy of Sciences, Warsaw, Poland, 1994.
23. J. R. Wang, X. Xiang, and W. Wei, "Linear impulsive periodic system with time-varying generating operators on Banach space," Advances in Difference Equations, vol. 2007, Article ID 26196, 16 pages, 2007.
24. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983.